Models of atmospheric transport can be used to interpret spatiotemporal differences in the observed concentrations of CO2 in terms of its surface exchange fluxes. Inversion of the atmospheric transport is the systematic search for both a flux field that yields an optimal match between modeled and observed concentrations and, equally importantly, the uncertainties in this inferred flux field. The present inversion study combines observations of the CO2 concentration at the global station network of the NOAA/CMDL in the 1980s with a representation of the atmospheric transport model TM2 by its Jacobian matrix, which has been previously computed by the adjoint model of TM2. This Jacobian matrix maps monthly fluxes on the approximately 8¿ latitude by 10¿ longitude horizontal model grid onto the resulting changes in the monthly CO2 concentration at every station. Since the number of observational sites is much smaller than the number of grid cells, the inverse problem is highly underdetermined. A unique solution is determined by including a priori information on the surface exchange fluxes derived from output of high-resolution models of both the terrestrial biosphere and the ocean, combined with statistics of fossil fuel burning and land use change. Performing a Bayesian synthesis inversion, for a target period in the 1980s, the average seasonal cycle and the mean annual magnitude of CO2 surface fluxes on the TM2 grid are inferred. The resulting simulated concentration compares well with independent observations. On a global scale, an oceanic sink of 1.5¿0.4 gigatons of carbon (GtC) is estimated. This sink is stronger in the northern than in the southern hemisphere. On a regional scale, however, the inferred exchange fluxes exhibit high uncertainty, indicating a low capacity of the global observational network to monitor regional trace gas emissions. These findings are relatively insensitive to the year of meteorological driving data, suggesting interannual changes in concentration should primarily result from source not transport changes. ¿ 1999 American Geophysical Union